A generalized fixed-point-free action
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KünyeGÜLOĞLU, İ.Ş., ERCAN, G. (2012). A generalized fixed-point-free action. Journal of Algebra and Its Applications, 12 (3), pp 1250172-1-1250172-4. http://dx.doi.org/10.1142/S0219498812501721.
In this paper we study the structure of a finite group G admitting a solvable group A of automorphisms of coprime order so that for any x ∈ CG(A) of prime order or of order 4, every conjugate of x in G is also contained in CG(A). Under this hypothesis it is proven that the subgroup [G, A] is solvable. Also an upper bound for the nilpotent height of [G, A] in terms of the number of primes dividing the order of A is obtained in the case where A is abelian.